Brigette,

Speaking as a member of Delta Sigma Theta, we are usually called Deltas, or possibly DST. I know at my campus there is the fraternity of Delta Tau Delta and they're called Delts. People not familiar with the frats./sororities, greek organizations, greek councils(i.e. IFC, NPHC, NPC) tend to get us confused.

From the info I've gathered, members of Delta Delta Delta are usually called Tri-Delts (a high school classmate of mine is one). I believe I've even heard the name 3D's.

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Sisterhood, Scholarship, & Service
Delta Sigma Theta Sorority, Inc.
"Intelligence is the Torch of Wisdom"